FIG. 17 is a block diagram of a typical variable speed driving apparatus according to the prior art for driving a plurality of induction machines. As shown in FIG. 17, the conventional variable speed driving apparatus includes an inverter 1, induction machines 2 (2.sub.1 . . . 2.sub.N), current detectors 3 (3.sub.u, 3.sub.v, 3.sub.w), speed detectors 4 (4.sub.1 . . . 4.sub.N), a detected current vector rotating device 5, a reference angular frequency operating device 6, a reference slip angular frequency operating device 8.sub.3, a reference magnetization current operating device 9, amplitude operating devices 30.sub.1 and 30.sub.2, a proportional plus integral operating device 31, an adder 12.sub.6, an integrator 13, a multiplier 14, and a reference voltage vector rotating device 15.sub.2.
The operation of the variable speed driving apparatus of FIG. 17 will now be described in detail. The reference magnetization current operating device 9 operates the reference value of a magnetization current i.sub.M * according to the following equation (1) based on the reference value of a primary magnetic flux .phi..sub.1 * inputted thereto: ##EQU1## where, L.sub.1 is the primary inductance per an induction machine and N the number of the induction machines.
The detected current vector rotating device 5 executes the transformation between the three-phase and two-phase systems according to the following equation (2) based on a reference phase value .theta.* and detected current values i.sub.u, i.sub.v and i.sub.w detected by the current detectors 3. ##EQU2##
The amplitude operating device 30.sub.1 operates a detected current amplitude I according to the following equation 3. And, the amplitude operating device 30.sub.2 operates a reference current amplitude I* according to the following equation 4 based on the reference magnetization current value i.sub.M * and reference magnetization current value i.sub.T * inputted thereto. ##EQU3##
The reference angular frequency operating device 6 outputs, based on the detected speed values .omega..sub.r1, .omega..sub.r2, .omega..sub.rN detected by the speed detectors 4.sub.1, 4.sub.2, 4.sub.N, the rotor angular frequency of the induction machine, the speed thereof is the lowest, in the motoring mode, and the rotor angular frequency of the induction machine the speed thereof is the fastest in the regenerative mode as a reference angular frequency .omega..sub.r.
The slip angular frequency operating device 8.sub.3 operates a reference slip angular frequency .omega..sub.s * according to the following equation 5: ##EQU4## wherein, R.sub.2 is a secondary resistance per an induction machine.
The adder 12.sub.6 calculates a reference angular frequency of the inverter (hereinafter referred to as a "primary reference angular frequency") .omega..sub.1 * by adding the result of the proportional plus integral operation of the difference between the reference current amplitude I* and the detected current amplitude I, the reference slip angular frequency .omega..sub.s * and the reference angular frequency .omega..sub.R.
The multiplier 14 calculates a reference voltage amplitude V* by multiplying the primary reference angular frequency .omega..sub.1 * and a primary reference magnetic flux .phi..sub.1 *.
The integrator 13 calculates the reference phase value .theta.* by integrating the primary reference angular frequency .omega..sub.1 *.
The reference voltage vector rotating device 15.sub.2 operates the three-phase reference voltage values i.sub.u *, i.sub.v * and i.sub.w * according to the following equation 6 based on the reference voltage amplitude V* and reference phase value .theta.* and outputs the calculated reference voltage values i.sub.u *, i.sub.v * and i.sub.w * to the inverter 1. ##EQU5##
By controlling the variable speed driving apparatus for driving the induction machines as described above, the primary magnetic fluxes of the induction machines bearing respective loads are regulated at a certain value and the current amplitudes at the reference value thereof.
In the conventional system described above, the reference voltage amplitude V* is determined by feeding forward the primary reference angular frequency .omega..sub.1 * and the primary reference magnetic flux .phi..sub.1 *. Due to this, the deviation of the actual voltage from the reference voltage amplitude becomes relatively high, since the reference voltage amplitude is small in the low speed region of the induction machines, that is when the primary reference angular frequency .omega..sub.1 * is small. As a result, the desired magnitude of magnetization current is not fed, the deviation of the primary magnetic flux from its reference value increases and the torque and rotating speed of the induction machine bearing a load lower.
In addition, the primary magnetic flux of the induction machine bearing a load is hardly adjusted at its reference value, and the torque and rotating speed of each induction machine cause lowering when certain unbalances exist between the loads of the respective induction machines, since the slip is not controlled in response to the state of load of each induction machine.
In view of the foregoing, it is an object of the present invention to provide a variable speed driving apparatus for driving a plurality of induction machines that facilitates minimizing the deviations of the primary magnetic fluxes of the induction machines bearing respective loads from the primary reference magnetic flux and preventing the torque and the rotating speed of each induction machine from lowering even in the low speed range or when certain unbalances exist between the loads of the respective induction machines.